Question

How do you find two consecutive odd integers whose sum is 196?

Answer 1

`97 and 99`

Explanation:

There is at least two ways of doing this: This is my approach

`color(blue)("Step 1")` Define a number so that it is always even

`" "`Let `n` be any number then `2n` is always even.

`color(blue)("Step 2")` Modify the defined number so that the result is always odd

`" "`If `2n` is always even then `2n+1` is always odd
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the first odd number be `2n+1`
Then the second odd number is `(2n+1)+2=2n+3`

Thus our given condition is such that:

`(2n+1)+(2n+3)=196`

`=>4n+4=196`

Subtract 4 from both sides

`=>4n=192`

Divide both sides by 4

`=>n=192/4=48`

But the first number is `2n+1 = 2(48)+1 = 97`

So the second number is `97+2=99`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check: `97+99= 196`

Answer 2

Another way

Explanation:

Let the first number be `n`
Let the second number be `n+2`

Then `n+n+2=196`

`2n+2=196`

Subtract 2 from both sides

`2n=194`

Divide both sides by 2

`n=194/2= 97`

The first number is 97 so the second is 97+2=99

`color(red)("Notice that the " 2n + 2" is of the same format as that in my")` `color(red)("other solution of "4n+4)`